I'm am not sure of your family's name lineage.... However my line of Thompson's were actually Torstensen's as they came from Norway and the names changed. I have a Hans Thompson who became Henry Thompson once stateside he was born in 1843 so I doubt he is your Henry. His father's last name was Torstensen.
Try Torsten Johansen or one of his siblings from Oppeland, Norway.
If they are from the Norway or Sweden line it's going to get harder and harder to track them the further you get as the last name "changes" with every generation. Traditional name pass down was actually a working mix of the fathers first name with their languages equivalent of son or daughter. So for instance all of Torsten Johansen's sons show up with the last name Torstensen, and his daughters are Torstendat or Torstendatter. It gets pretty confusing prior to the 1830s when mass immigration to America started for most of our ancestors.
My Ancestry family tree
If you would like to look at my tree and see if you can find any answers or similarities you are welcome to it we have the Thompson line traced back pretty far. My mom was a Thompson. The link I added should take you to a viewable tree on Ancestry. If you search for "Christina Elizabeth Thompson" to then you can follow back from there. Once you get past "Hans (Henry) Thompson you'll start to see the name variations I was talking about.
I hope this helps in some way.